Propensity score adjusted method for missing data

Abstract

Propensity score adjustment is a popular technique for handling unit nonresponse in sample surveys. When the response probability does not depend on the study variable that is subject to missingness, conditional on the auxiliary variables that are observed throughout the sample, the response mechanism is often called missing at random (MAR) or ignorable, and the propensity score can be computed using the auxiliary variables. On the other hand, if the response probability depends on the study variable that is subject to missingness, the response mechanism is often called not missing at random (NMAR) or nonignorable, and estimating the response probability requires additional distributional assumptions about the study variable. In this dissertation, we investigate the propensity-score-adjustment method and the asymptotic properties of the estimators under two different assumptions, MAR and NMAR. We discuss some asymptotic properties of propensity-score-adjusted(PSA) estimators and derive optimal estimators based on a regression model for the finite population under MAR. An optimal propensity-score-adjusted estimator can be implemented using an augmented propensity model. Variance estimation is discussed, and the results from two simulation studies are presented. We also consider the NMAR case with an explicit parametric model for response probability and propose a parameter estimation method for the response model that is based on the distributional assumptions of the observed part of the sample instead of making fully parametric assumptions about the population distribution. The proposed method has the advantage that the model for the observed part of the sample can be verified from the data, which leads to an estimator that is less sensitive to model assumptions. Under NMAR, asymptotic properties of PSA estimators are presented, variance estimation is discussed, and results from two limited simulation studies are presented to compare the performance of the proposed method with the existing methods.